Re: TI-92, HELP! Significative numbers!!!

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Re: TI-92, HELP! Significative numbers!!!

Ray Kremer wrote:
>
> >Apart from that, he was talking about significant digits. Very simple
> >thing, just set FIX 2 as said before, then choose:
> >Exponential Format = Scientific
> >
> >Like this,
> >17000  --> 1.70E4
> >123.45 --> 1.23E2
> >1.7    --> 1.70E0
> >0.001  --> 1.00E-3
> >
> >and so forth. You always get 3 significant digits.
>
> You have also demonstrated a lack of knowledge as to what significant digits
> really means.  Number of decimal places IS NOT the same thing as significant
> digits.  For instance, using your own examples:
> 17000 has two sig figs ---->   1.7e4
> 123.45 has five sig figs --->  1.2345e2
> 1.7 has two sig figs ---> 1.7e0
> 0.001 has one sig fig ---> 1.e-3
>
> The thing none of you quite realise is that the rounding for sig figs must be
> determined on a case by case basis.  You can't just say, "I will want three
> sig figs for all my calculations."  No.  It doesn't work that way.  You
> must look at the number of sig figs in the numbers you are calculating, and
> from that determine the number of sig figs that the answer needs to be
> rounded to.  That is why the human operator must to this by himself.  The
> TI-92 is not programed to do sig figs, and such a thing would be very hard
> to program, while it's not so hard to just do it by yourself, as long as
> you actually know how.

DUH! I thought I'd give some advice to people who know the number of
significant digits they want, like if the calculus exercise says "give 3
decimals". To be closer to reality, or to estimate the number of
significant digits of a function f(x,y,z,w,...) you'd have to proceed
thus:

1. estimate the uncertainty on each one of the values of x,y,z,w,...,
   and call them Dx,Dy,Dz,Dw,...
2. evaluate Df = the uncertainty of f(x,y,z,w):

   Df = |df/dx|*Dx + |df/dy|*Dy + |df/dz|*Dz + ...

   where df/dx etc. are partial derivatives.

Let's do an example: suppose you want to know the area of a sheet of
paper. In that case, a = x * y, where a is the area and x,y are the
length&width of the paper. Suppose x = 21 cm, Dx = 1 cm, y = 30 cm, Dy =
1 cm, i.e. you measured x and y with an uncertainty of 1 cm.
   da/dx = y
   da/dy = x
thus a = x * y = 6300 cm2 and
Da = y * Dx + x * Dy = 51 cm2
Finally, the uncertainty of the value of the area is 51 cm2, so it would
be reasonable to say that the paper has an area of (6.30 +/- 0.05)E+3
cm2.
Like this, it is easy to estimate the number of significant digits of
complicated results; the partial derivatives are very simple on the
TI-92 with the italic d key.
This procedure works as long as the uncertainties Dx,Dy etc remain small
and the partial derivatives are not zero, as well as the second, third
etc. derivatives remain small. This just means that you have to have
more sophisticated formulas from time to time, but normally the one I
explained works pretty well.

        Roman.
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